Method for high precision printing of patterns

ABSTRACT

The present invention includes a method to print patterns with improved edge acuity. The method for printing fine patterns comprises the actions of: providing an SLM and providing a pixel layout pattern with different categories of modulating elements, the categories differing in the phase of the complex amplitude.

FIELD OF THE INVENTION

The invention relates to the printing of patterns with high precision,in particular to printing of microlithographic pattern such as patternson photomasks and wafers. The invention may also be applied to otherprinting, such as for the formation of optical devices, electronicinterconnects and even to decorative printing and security printing.

The invention is particularly suited to but not limited to opticalprinting using partially coherent light, such as from excimer and atomiclasers and from EUV light sources. In a preferred embodiment it isapplied to a maskless scanner for exposure of patterns ontosemiconductor wafers without the need for reticles or masks.

BACKGROUND OF THE INVENTION

In the past, integrated circuits have been manufactured more or lesssolely by using a number of masks or reticles comprising a pattern of alayer in said integrated circuit. In today's integrated circuits thenumber of layers could be larger than 30. Said Masks or reticles may beprepared in lithographical manner by using for example electron beams orlaser beams for exposing a layer of material sensitive for the type ofbeam chosen. The mask material is most commonly transmissive on top ofone of its sides a thin layer of opaque material is attached. In saidthin material the pattern of one layer of said integrated circuit iscreated. The mask has typically N times larger pattern than the patternto be printed on the semi-conducting substrate for forming saidintegrated circuit. The reduction in size is performed in a stepper,which uses the mask(s) for forming said integrated circuit.

More recently, the need to manufacture integrated circuits by meansother than using a conventional mask has developed for a number ofreasons, for example the price of manufacturing mask(s) has increaseddue to its complexity to manufacture, small-scale development whichneeds very small series of integrated circuits, etc.

Unfortunately, all of the present known techniques for formingintegrated circuits without using conventional masks or reticles havedrawbacks and limitations. For example, most direct-writers known in theart are based on electron beams, typically so called shaped beams, wherethe pattern is assembled from flashes, each defining a simplegeometrical figure. Other systems are known which use raster scanning ofGaussian beams. By using a conventional mask writer, which uses beams ofelectrons or laser beams for forming the pattern on a workpiece, islimited to relatively low scanning speeds, and, perhaps worst of all,can only scan a single dimension.

SLM writers disclosed in other patent applications, such as WO 01/18606and U.S. patent application Ser. No 09/954,721 by the same assignees asthe present invention and hereby incorporated by reference is related toraster scanning in the sense that it permits a bitmap pattern, butdistinct by printing an entire frame of pattern in one flash instead ofbuilding the pattern from individual pixels.

A spatial light modulator (SLM) comprises a number of modulatorelements, which can be set in a desired way for forming a desiredpattern. Reflective SLMs may be exposed to any kind of electromagneticradiation, for example DUV or EUV for forming the desired pattern on themask.

The same assignee has in a number of previous patent applications, forinstance WO 99/45440 and WO 99/45441, disclosed pattern generatortechnology for precision printing of submicron patterns. Typically theembodiments taught in said applications use SLMs with analog modulation.The modulating elements are micromechanical mirrors that are capable ofgradually move from a resting to a fully actuated state in response toan electronic drive signal, and the elements form one or two-dimensionalarrays of modulating elements. A pattern defined in an input database israsterized to a bitmap were each pixel can have several states between alightest and a darkest state.

What is needed is a method and apparatus, which creates pattern on aworkpiece using a programmable reticle or mask, such as a spatial lightmodulator, capable to create patterns with high feature edge acuity.What is also needed is a method and apparatus capable to pattern featureboundaries with high accuracy of placement.

SUMMARY OF THE INVENTION

Accordingly, it is an object of the present invention to provide amethod of patterning a workpiece, which overcomes or at least reducesthe above-mentioned problem of creating fine patterns with high acuityand high accuracy of placement of feature boundaries.

This object, among others, is according to a first aspect of theinvention attained by a method for printing fine patterns with highprecision Said method comprising the actions of providing an SLM havingan array of modulator elements, providing an electromagnetic radiationsource, collimating radiation from said radiation source to createpartially coherent illumination of said SLM with a coherence length thatis larger than half the pitch of the modulating elements in the SLM,creating a negative complex amplitude with at least one modulatorelement.

Other aspects of the present invention are reflected in the detaileddescription, figures and claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts the general layout of an SLM pattern generator.

FIG. 2 depicts in a perspective view a prior art square mirror.

FIG. 3 depicts the reflected intensity and complex amplitude as functionof the tilt angle of the mirror element.

FIG. 4 depicts the real and imaginary part of the complex amplitude forthe mirror element depicted in FIG. 2.

FIG. 5 a-b depict the mirror comprising reference surface and surfaceelement.

FIG. 6 a-b illustrate the relation between coherence length and angularspread.

FIG. 7 a illustrates a prior art method of patterning a substrate onlyusing positive complex amplitude.

FIG. 7 b illustrates in inventive method of patterning a substrate usingpositive and negative complex amplitudes.

FIG. 8 a-c depict different ways of creating data to be fed to an SLM.

FIG. 9 a depicts a clear feature in vector data.

FIG. 9 b depicts a rasterized representation of the vector data in FIG.9 a with the off grid edge enhanced by extra exposure on the new brightpixel and negative black on the dark pixel.

FIG. 9 c depicts a screen shot of resist edges from a Solid-C simulator.

FIG. 9 d depicts a screen shot showing the position of the center of theclear feature vs. dose with and without enhancement of the off-gridedge.

FIG. 10 a depicts an alternating phase shift mask.

FIG. 10 b depicts SLM pixels with complex amplitude reflectivitycorresponding to the alternating phase shift mask in FIG. 10 a.

FIG. 11 a depicts a 2×2 array of mirrors with different phasecharacteristics.

FIG. 11 b illustrates a complex amplitude reflectivity as function oftilt of the mirror.

FIG. 12 a-e illustrate 2×2 arrays of mirrors as depicted in FIG. 11 aonly differing in the way they are tilted.

FIG. 13 a-13 d illustrate the correspondence between different areas ofmasks/reticles and different areas of a SLM.

FIG. 14 a depicts an embodiment of a mirror.

FIG. 14 b depicts the complex amplitude trajectory of the mirror in FIG.14 a.

FIG. 14 c depicts a pixel transfer function of the mirror in FIG. 14 a.

FIG. 15 a depicts an embodiment of a mirror.

FIG. 15 b depicts the complex amplitude trajectory of the mirror in FIG.15 a.

FIG. 15 c depicts a pixel transfer function of the mirror in FIG. 15 a.

FIG. 16 a depicts an embodiment of a mirror.

FIG. 16 b depicts the complex amplitude trajectory of the mirror in FIG.16 a.

FIG. 16 c depicts a pixel transfer function of the mirror in FIG. 16 a.

FIG. 17 a depicts an embodiment of a mirror.

FIG. 17 b depicts the complex amplitude trajectory of the mirror in FIG.17 a.

FIG. 17 c depicts a pixel transfer function of the mirror in FIG. 17 a.

FIG. 18 a depicts an embodiment of a mirror.

FIG. 18 b depicts the complex amplitude trajectory of the mirror in FIG.18 a.

FIG. 18 c depicts a pixel transfer function of the mirror in FIG. 18 a.

FIG. 19 a depicts an embodiment of a mirror.

FIG. 19 b depicts the complex amplitude trajectory of the mirror in FIG.19 a.

FIG. 19 c depicts a pixel transfer function of the mirror in FIG. 19 a.

FIG. 20 a depicts an embodiment of a mirror.

FIG. 20 b depicts the complex amplitude trajectory of the mirror in FIG.20 a.

FIG. 20 c depicts a pixel transfer function of the mirror in FIG. 20 a.

FIG. 21 a depicts an embodiment of a mirror.

FIG. 21 b depicts the complex amplitude trajectory of the mirror in FIG.21 a.

FIG. 21 c depicts a pixel transfer function of the mirror in FIG. 21 a.

FIG. 22 a depicts an embodiment of a mirror.

FIG. 22 b depicts the complex amplitude trajectory of the mirror in FIG.22 a.

FIG. 22 c depicts a pixel transfer function of the mirror in FIG. 22 a.

FIG. 22 d illustrates an array of pixel as illustrated in FIG. 22 a.

FIG. 23 a depicts an embodiment of a mirror.

FIG. 23 b depicts the complex amplitude trajectory of the mirror in FIG.23 a.

FIG. 23 c depicts a pixel transfer function of the mirror in FIG. 23 a.

FIG. 24 a depicts an off grid filter implementation.

FIG. 24 b depicts an off grid filter.

FIG. 25 a depicts an embodiment of a mirror.

FIG. 25 b depicts the complex amplitude trajectory of the mirror in FIG.25 a.

FIG. 25 c depicts a pixel transfer function of the mirror in FIG. 25 a.

FIG. 26 a depicts an embodiment of a mirror.

FIG. 26 b depicts the complex amplitude trajectory of the mirror in FIG.26 a.

FIG. 26 c depicts a pixel transfer function of the mirror in FIG. 26 a.

FIG. 27 a depicts an embodiment of a mirror.

FIG. 27 b depicts the complex amplitude trajectory of the mirror in FIG.27 a.

FIG. 27 c depicts a pixel transfer function of the mirror in FIG. 27 a.

FIG. 28 a depicts an embodiment of a mirror.

FIG. 28 b depicts the complex amplitude trajectory of the mirror in FIG.28 a.

FIG. 28 c depicts a pixel transfer function of the mirror in FIG. 28 a.

FIG. 29 a depicts an embodiment of a mirror.

FIG. 29 b depicts the complex amplitude trajectory of the mirror in FIG.29 a.

FIG. 29 c depicts a pixel transfer function of the mirror in FIG. 29 a.

FIG. 30 a depicts an embodiment of a mirror.

FIG. 30 b depicts the complex amplitude trajectory of the mirror in FIG.30 a.

FIG. 30 c depicts a pixel transfer function of the mirror in FIG. 30 a.

FIG. 31 a depicts an embodiment of a mirror.

FIG. 31 b depicts the complex amplitude trajectory of the mirror in FIG.31 a.

FIG. 31 c depicts a pixel transfer function of the mirror in FIG. 31 a.

FIG. 32 a depicts a slanted line and its rasterized pixel representation

FIG. 32 b depicts the exposure dose as a function of the position ofsaid slanted line.

FIG. 33 a illustrates the contrast as a function of spatial frequencyfor on-grid pixels and off-grid pixels without any grid filter.

FIG. 33 b illustrates the contrast as a function of spatial frequencyfor on-grid pixels and off-grid pixels with an off-grid filter.

FIG. 33 c illustrates the contrast as a function of spatial frequencyfor on-grid pixels and off-grid pixels with off-grid filter and globaledge enhancement.

FIG. 34 illustrates a diagram showing contrast as a function of pixelnumber.

FIG. 35 a-b illustrate an embodiment of an off-grid correction filteraccording to the present invention.

FIG. 36 illustrates resulting LUT functions for a gray and dark pixel.

FIG. 37 a-39 b illustrate calculated improvements due to the inventiveoff-grid filter.

FIG. 40 a-b illustrate another embodiment of an off-grid correctionfilter according to the present invention.

FIG. 41 a illustrates an SLM with amplitude transmission modulatedpixels.

FIG. 41 b illustrates an ideal pattern from a binary mask.

FIG. 42 illustrates look up tables for pixels on and outside an edge.

FIG. 43 illustrates performance comparison illumination table and gridfilter (off-grid filter).

FIG. 44 a illustrates an uncompensated edge in a pattern.

FIG. 44 b illustrates a compensated edge in a pattern.

FIG. 45 a illustrates an SLM with amplitude transmission modulatedpixels.

FIG. 45 b illustrates an ideal pattern from a binary mask.

FIG. 46 illustrates look up tables for pixels on and outside an edge.

DETAILED DESCRIPTION

The following detailed description is made with reference to thefigures. Preferred embodiments are described to illustrate the presentinvention, not to limit its scope, which is defined by the claims. Thoseof ordinary skill in the art will recognize a variety of equivalentvariations on the description that follows.

Spatial light modulators come in two varieties, a deflection type and aphase type. The differences between them may in a particular case withmicromirrors seem small but the phase SLM extinguishes the beam in aspecular direction by destructive interference, while a pixel in adeflection SLM deflects the specular beam geometrically to one side sothat it misses an aperture of an imaging lens. The deflection type SLMhave pixels which operate digitally, i.e., said pixels may be set to twostates only fully on and fully off. Said kind of pixels are said to beoperated in a digital mode. The phase type SLM have pixels which operatein an analog mode, i.e., said pixels may be set to a numerous statesbetween fully off and fully on. In one embodiment there are 63 statesbetween fully off and fully on, i.e., 65 states in total. A degree ofdeflection of a micro-mirror determines which state said mirror would bein. All different states correspond to different gray-levels, which maybe used to move edges of features to be printed.

FIG. 1 depicts the general layout of an SLM pattern generator. Aspectsof an SLM pattern generator are disclosed in the related-pending patentapplications identified above. The workpiece to be exposed sits on astage 112. The position of the stage is controlled by precisepositioning device, such as paired interferometers 113.

The workpiece may be a mask with a layer of resist or other exposuresensitive material or, for direct writing, it may be an integratedcircuit with a layer of resist or other exposure sensitive material. Inthe first direction, the stage moves continuously. In the otherdirection, generally perpendicular to the first direction, the stageeither moves slowly or moves in steps, so that stripes of stamps areexposed on the workpiece. In this embodiment, a flash command 108 isreceived at a pulsed excimer laser source 107, which generates a laserpulse. This laser pulse may be in the deep ultraviolet (DUV) or extremeultraviolet (EUV) spectrum range. The laser pulse is converted into anilluminating light 106 by a beam conditioner or homogenizer.

A beam splitter 105 directs at least a portion of the illuminating lightto an SLM 104. The pulses are brief, such as only 20 ns long, so anystage movement is frozen during the flash. The SLM 104 is responsive tothe datastream 101, which is processed by a pattern rasterizer 102. Inone configuration, the SLM has 2048×512 mirrors that are 16×16 μm eachand have a projected image of 80×80 nm. It includes a CMOS analog memorywith a micro-mechanical mirror formed half a micron above each storagenode.

The electrostatic forces between the storage nodes and the mirrorsactuate the mirrors. The device works in diffraction mode, not specularreflectance, and needs to deflect the mirrors by only a quarter of thewavelength (62 nm at 248 nm) to go from the fully on-state to the fullyoff-state. To create a fine address grid the mirrors are driven to on,off and 63 intermediate values. The pattern is stitched together frommillions of images of the SLM chip. Flashing and stitching proceed at arate of 1000 stamps per second. To eliminate stitching and other errors,the pattern is written four times with offset grids and fields.Furthermore, the fields may be blended along the edges. The mirrors areindividually calibrated. A CCD camera, sensitive to the excimer light,is placed in the optical path in a position equivalent to the imageunder the final lens. The SLM mirrors are driven through a sequence ofknown voltages and the response is measured by the camera. A calibrationfunction is determined for each mirror, to be used for real-timecorrection of the grey-scale data during writing. In the data path, thevector format pattern is rasterized into grey-scale images, with greylevels corresponding to dose levels on the individual pixels in the fourwriting passes. This image can then be processed using image processing.The final step is to convert the image to drive voltages for the SLM.The image processing functions are done in real time using programmablelogic. Through various steps that have been disclosed in the relatedpatent applications, rasterizer pattern data is converted into values103 that are used to drive the SLM 104.

In this configuration, the SLM is a diffractive mode micromirror device.A variety of micromirror devices have been disclosed in the art. In analternative configuration, illuminating light could be directed througha micro-shutter device, such as in LCD array or a micromechanicalshutter.

An SLM pattern generator, such as a mask writer or direct writer, thatuses a grey-scale sampled image enables a variety of enhancementschemes. The grey value of each pixel is an area sample value of thepattern. Taking into account the imaging properties of the tool and adesired response, such as a specific corner radius, adjustments of theexposure values in a predetermined vicinity of a corner feature can beused to mimic or match the properties of another pattern generator, suchas the exposed corner radius and corner pull back. The adjustment recipecan be adapted to match, for instance, another mask writer. To do this,exposed pattern properties in resist on workpieces of the two patterngenerators can be compared. The comparison can be based on eithersimulation, developed resist or latent images in resist. Comparison ofthe exposed patterns allows adjustment of one or more process controlparameters until the exposed patterns essentially match.

Data is modified in the raster domain of at least one of the patterngenerators according to the process control parameters, rather thanmodifying vector-based pattern data in the design domain. The processcontrol parameters may relate to corner feature exposure properties.

A mirror consisting of an essentially square mirror plate pivotingaround an axis defined by torsion hinges in the plane of the mirror, seeFIG. 2, modulates the beam from fully-on to fully-off. The fully-offstate depends on the illumination of the mirror. The illuminator definesan angular subtense, which in turn determines the lateral coherence ofthe illumination light. The lateral coherence is in this sense differentfrom the temporal coherence.

Temporal coherence usually means that the radiation comes from a laser,but lateral coherence can be produced by any light source made toilluminate a surface under a small enough angular spread. This is wellknown in the art and described in text books such as Born and Wolf:Principles of optics.

The notion of lateral coherence length is significant to thisdiscussion. The lateral coherence length is of the order of the typicalor center wavelength of the radiation divided by the angular spread ofthe illuminating beam. Projectors known in prior art (such as those usedby Texas Instruments in their DLP technology and Daewoo in their AMAprojectors) have used a high angular spread leading to a coherencelength smaller than the size of an individual mirror element, see FIG. 6a. With this type of illumination each mirror acts as an independentspecular reflector. The pattern generators disclosed and made by theapplicant do on the other hand use a small angular spread in theilluminating beam, giving a coherence length that is of the same orderas a mirror element or larger, see FIG. 6 b. The effect is thatdifferent areas of a mirror interact by interference and thatdestructive or constructive interference effects also occur betweenmirror elements. The two different types of projectors will be calledincoherent and partially coherent projectors respectively, the termprojectors in this case meaning a generic image-forming system using anSLM, an illuminator and a projection system including a spatial filter.Incoherent projector are defined by the property of not forming apartially or fully coherent image, which can be due to the illuminationmode, but also to a superposition of pixels at different times. The casewhere two or more fully coherent images are superimposed sequentially isconsidered as partially coherent.

Under illumination where the lateral coherence extends over a fullmirror, the mirror does not act as a simple analog light valve any more,but a complex amplitude modulator. The complex amplitude is related tothe electric field of the radiation, while the intensity is more akin tothe energy density or energy flow. An interesting property of thecomplex amplitude is that it can have a negative sign, see curve 320 inFIG. 3, while the intensity (energy flow) is always positive, see FIG.310 in FIG. 3. With the illumination scheme that produces laterallycoherent light it is possible for one light beamlet to cancel the lightof another one. The consequence is that suitably conditioned radiationcan be added to reduce the light intensity at a point were it is desiredto be dark, thereby improving contrast.

The square mirror 220 tilting along one of its axis 210 acts as aspecular mirror when it is parallel to the plane of the surface. When itis successively tilted out of the plane the edges move out of phase andbecome more and more destructive, giving perfect extinction of the lightwhen they have a phase shift of +/−180 degrees in reflection, see point330. But if the mirror is tilted more they continue further into thenegative and the entire mirror gives negative complex amplitude. FIG. 3shows this. The complex amplitude reflectivity of a mirror R can becalculated as the double integral over the mirror surface S 510 of thecomplex amplitude reflection r of every surface element Ds 520.

$R = \frac{\oint\limits_{S}{r*{\mathbb{d}s}}}{\oint\limits_{S}{\mathbb{d}s}}$

The denominator is the reflecting area of the mirror. In a more generalcase with varying reflectivity the expression can be generalized toinclude differences between the surface elements. In the most simplecase with a perfectly reflecting surface the complex amplitudereflectivity r of a surface element is

r=e^(−i(4πh/λ)), where h 530 is the height of the mirror surface 510above a reference surface 540. The reference surface 540 can be chosenarbitrarily (and the complex amplitude reflectivity R can be multipliedwith an arbitrary but constant phase factor e^(iφ)) with no change inthe physics. For definiteness the reference surface 540 is chosen hereto be the plane through the hinges 550, giving R=1 for a flat non-tiltedmirror.

FIG. 3 shows the reflected intensity and complex amplitude as functionsof the tilt angle. With a symmetric mirror making a perfect pivotingaction around a symmetry axis the imaginary part of R is always zero.The real part of R varies from 1.00 through 0.00 to a minimum of −0.22.For higher tilt angles it becomes positive again and approaches R=0 inthe limit, see FIG. 4. For the square mirror the tilt for the first nullR=0 occurs when the tilt is half a wavelength from one side to the otherof the mirror, see point 330 in FIG. 3. It is easy to see why this giveszero: because it is a reflective device the phase in the light beamvaries from −180 to +180 degrees. For each surface element with phase □there is another surface element with phase □+180 degrees, thus thereflection from every surface element is cancelled. Incident energy isdiffracted away from the specular direction and does not find its waythrough at least one stop in projection optics.

The pattern generators developed by the applicant have used thereflectivity range 0<R<1 to print a pattern, where R=0 is used for areaelements intended to be unexposed and R=1−□ is used for exposed areas.The term □, which is typically 10%, is introduced to allow even exposureeven in the presence of some statistical variation in R from mirror tomirror.

A fine address grid, much finer than that given by the mirrors, iscreated by giving mirrors at the edge intermediate values. These valuesare interpolated between exposed and unexposed mirror tilts, times anon-linear function, the illumination table. The illumination table isimplemented as a look-up table that is pre-computed or determinedexperimentally. The shape of the illumination function depends on anumber of factors, most important on the projected mirror size comparedto the optical resolution and the angular spread of the illuminatingradiation.

In the incoherent projector the complex quantity R does not have anymeaning, since the surface integrals only have meaning for lateralcoherence lengths on the scale of the mirror size.

The quantity R is defined as a complex amplitude reflectivity in apartially coherent projector, not as the normal intensity reflectivityrelevant in an incoherent projector.

As described above R is a complex number and may have any value as longas |R|≦1. With the symmetrical mirrors Im (R)=0, but R can still benegative, and does in fact do so for tilts larger than half awavelength. This can be used for image enhancement that is not possiblein incoherent projectors. FIG. 4 depicts an example of a complexamplitude reflectivity curve 40.

One type of image enhancement is achieved by selecting the a value ofR<0 for areas that are intended to be unexposed. A typical value isR=−0.15. This corresponds to an intensity reflection of 2.25% and givesa background exposure of 2.25% is areas that are intended to beunexposed. However, 2.25% is not enough to cause the photo resist (ormore generally the photosensitive surface) to develop, since it has adevelopment threshold typically around 30%. But exposed features getcrisper edges since the −0.15 reflectivity, having phase 180 degrees,cancels light with phase 0 degrees at the perimeter of the exposedfeatures. The dark areas get larger, the edge steeper and if the size iscompensated with more dose the edge enhancement is even furtherenhanced.

FIG. 7 a illustrates a prior art method of patterning features using anSLM. SLM pixels inside a feature to be patterned, hatched pixels in FIG.7 a, have a complex amplitude reflectivity R equal to 0. Pixels outsidesaid feature, non-hatched pixels in FIG. 7 a, have a complex amplitudereflectivity being equal to 1. The illustrated example in FIG. 7 a, havefeature edges coinciding with a pixel grid of the SLM. For this reasonpixel elements defining the edge of the feature also have complexamplitude reflectivity equal to 0. If, however the feature edge fallsbetween the pixel grid, said complex amplitude reflectivity will be anyvalue in the range of 0<R<1. The value of R is depending on theplacement of said edge.

In FIG. 7 a a graph 710 represents the complex amplitude of reflectivityR taken along a line A-A. FIG. 7 b illustrates the inventive method forcreating features with increased edge acuity and placement accuracy.Here the pixels inside the feature, hatched pixels in FIG. 7 b, havecomplex amplitude less than 0, i.e., a negative value. A graph 720represents the complex amplitude reflectivity taken along line B-B.Inserted in FIG. 7 b is also the graph representing the intensity ofreflectivity |R|2. The use of negative R is analogous to the use ofso-called attenuated or embedded phase shifting masks in lithography.The value of R to be selected at will between 0 and a minimum value. Atfirst sight is seems that the minimum value is −0.218. This correspondsto 4.77% exposure, less than 6% attenuated masks used instate-of-the-art lithography.

Closer analysis shows that it is not the maximum exposure dose E that iscreating the effect but the value of the complex amplitude A in blackareas relative to the complex amplitude in bright ones. Disregardingagain a constant phase factor together with some prefactors that may bepresent.

A=R*√{square root over (E)}, where E is the exposure dose. Using anR<1.00 as described above leads to a higher exposure dose and theminimum also gets larger in proportion.

The minimum value of A for the square mirror is

$A_{\min} = {A_{exposed}*\frac{- 0.218}{\left( {1 - ɛ} \right)}}$

If we choose □=15% we get Amin=−0.256. This corresponds to an intensityof 6.6%, which is with a small margin equivalent to theindustry-standard 6% attenuated mask blanks. In an SLM writer the doseand the mirror tilts are under software control, so even larger ∈ can beused to get more negative amplitude. The restrictions are twofold:first, increasing the dose causes problems by itself, such as thecreation of more stray light. Second, imperfections in the mirrors getmagnified. However, these limitations are purely practical and the useof high □ and strongly negative R cannot be ruled out beforehand.

In previously implemented rasterizers the value of the pixel of mirrorat the feature edge has been calculated as an interpolation between theexposed and unexposed value based on how much of the pixel falls on theexposed feature. Before it is converted to drive signals for the SLM.

Image modulator elements it is corrected through the illumination tableLUT as described above.

In a further improvement a digital filter (term taken in a wide sense)is applied to the rasterized data to enhance edges and corners. Thefilter can be designed and implemented in many ways: linear ornon-linear, based on rules or mathematical operations. One of thesimplest rules is that whenever a pixel has a neighbor that is gray(i.e. has an intermediate value) the current pixel is enhanced, so thata white pixel gets whiter (more positive) and a black pixel gets blacker(less positive). In an incoherent projector the range of pixel values islimited to zero to full illumination, in the partially coherentprojector the pixel value has the range Amin<A<Amax where Amin can benegative.

FIG. 8 a illustrates the way drive signals are converted before beingfed to the SLM according to a first embodiment. Vector data is fracturedand rasterized according to well-known principles in the art. Edgefilters are applied according to methods described above and below. Theillumination table and mirror look up table is used before the finaldrive signal is created. In FIG. 8 b another embodiment is illustratedwhich uses two illumination tables instead of one. By doing so better CDcontrol may be achieved. FIG. 8 c illustrates yet another embodimentwhich splits the rasterized data into two parallel branches. A firstbranch uses a first and second illumination table 1 a, 1 b, and a highpass filter. A second branch uses a third and a fourth illuminationtable and a low pass filter. Data split into high frequency and lowfrequency data. One could also split the data into x and y branches,meaning that a first branch is optimized for data only in a y directionand a second branch optimizes data only in an x direction, where x and ycould be horizontal and vertical data.

The availability of negative pixel values in the partially coherentprojector gives more corrective power than positive-only. In particularit makes it possible to improve both resolution and contrast of finelines.

The digital image enhancements are comparatively easy to make in thebitmap domain. The pattern is typically input in a hierarchical vectorformat such as GDSII, MIC or OASIS. The ordering of data in the inputfile obeys no rules and a contiguous geometrical feature can be formedfrom several elements from different parts of the hierarchicalstructure. The hierarchy is flattened and all neighbor and overlaprelations are resolved when the bitmap is created. Thus the bitmapoperations need only look at local information, in contrast tooperations in the vector format.

A close look at the rasterizing process shows that it acts as a low-passfilter at some grid positions and not at others. When the edge is placedrelative to the edge so that an intermediate pixel value is created someof the edge acuity of the optical system is lost. This can berepresented with a low-pass filter, FIG. 32 a, 32 b, at other gridpositions where the edge is represented without an intermediate value noloss of acuity occurs. FIG. 32 a illustrates a slanted line 325 andcorresponding pixel data. A cut at A illustrates that said slanted line325 lies on grid. FIG. 32 b illustrates exposure dose as function ofposition. Graph A represents when the line is n grid and graph Brepresents when the line is off-grid, such as at A cut at B in FIG. 32a. FIG. 32 b illustrates that the graph is steeper for on grid positioncompared to off-grid positions.

FIG. 33 a illustrates contrast versus spatial frequency for on-gridpixels and off-grid pixels without any grid filter. The upper sequenceillustrates on-grid pixels and the lower sequence illustrates off-gridpixels. Here it is clearly illustrated that off-grid pixels, i.e., afeature edge that does not fall on the grid position for SLM pixels, actas a low pass filter. The optics in a pattern generator also works as alow pass filter. The combination of the optics and the on grid gives animage with a certain low pass characteristic. The combination of offgrid and the optics gives an image with another low pass characteristic(solid line) than what is expected, dotted line in FIG. 33 a.

FIG. 33 b illustrates the contrast as a function of spatial frequencyfor on-grid pixels and off-grid pixels with an off-grid filter. Here theoff-grid filter counteracts the low pass performance caused by the offgrid position. The off grid image has equivalent contrast versus spatialfrequency performance as the on grid image.

FIG. 33 c illustrates the contrast as a function of spatial frequencyfor on-grid pixels and off-grid pixels with off-grid filter and globaledge enhancement. The global filter enhances the contrast versus spatialfrequency characteristics in that the graph is steeper in both theon-grid and off-grid image compared to the graph in the on-grid andoff-grid image without said global filter (dotted graph). A steeperfunction will enhance edge placement accuracy and edge acuity.

FIG. 34 illustrates a diagram showing contrast as a function of pixelnumber. Pixels 341 illustrates the area bitmap for a certain pattern.Pixels 343 illustrates said pixels with an off-grid filter applied.Pixels 345 illustrates convolved pixels, i.e., with a global edgeenhancement. The global enhancement enhances all edges, while theoff-grid filter enhances only edges with an intermediate value for theedge pixel.

FIG. 10 a illustrates an alternating phase shift mask. The leftmost areais phase shifted 180 degrees relative to the rightmost area. The middlearea is dark. A represenation of said alternating phase shift mask ascomplex amplitude reflectivity values is illustrated in FIG. 10 b. Hereit is illustrated that the transition from dark to bright is notperformed in one step bur through an intermediate step. −1 correspondsto the 180 degrees area, +1 corresponds to the 0 degree area, 0corresponds to the dark area, −0.6 corresponds to the leftmosttransition step and 0.3 corresponds to the rightmost transition step.

The remedy is what will be called an off-grid filter, a filter thatdetects that the edge is at an interpolated position and sharpens theedge by an appropriate amount to counteract the softening action of therasterization. Edge sharpening by itself is well known in the imageprocessing, although it is not common to have negative values available.One edge-sharpening operation is convolution with a partially derivativekernel. Such a kernel can look as follows:

$D = \begin{pmatrix}{- 0.1} & {- 0.2} & {- 0.1} \\{- 0.2} & {+ 2.2} & {- 0.2} \\{- 0.1} & {- 0.2} & {- 0.1}\end{pmatrix}$

Convolved with a bitmap Bin it produces a new bitmap BoutB_(out)=B_(in){circle around (x)}D

The following is an example bitmap and how the edge is enhanced by theconvolution

$B_{i\; n} = \begin{pmatrix}\ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\\ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\\ldots & {100\mspace{11mu}\%} & {100\mspace{11mu}\%} & {100\mspace{11mu}\%} & {50\;\%} & {0\;\%} & {0\;\%} & {0\;\%} & \cdots \\\cdots & {100\mspace{11mu}\%} & {100\mspace{11mu}\%} & {100\mspace{11mu}\%} & {50\;\%} & {0\;\%} & {0\;\%} & {0\;\%} & \cdots \\\cdots & {100\mspace{11mu}\%} & {100\mspace{11mu}\%} & {100\mspace{11mu}\%} & {50\;\%} & {0\;\%} & {0\;\%} & {0\;\%} & \cdots \\\cdots & {100\mspace{11mu}\%} & {100\mspace{11mu}\%} & {100\mspace{11mu}\%} & {50\;\%} & {0\;\%} & {0\;\%} & {0\;\%} & \cdots \\\cdots & {100\mspace{11mu}\%} & {100\mspace{11mu}\%} & {100\mspace{11mu}\%} & {50\;\%} & {0\;\%} & {0\;\%} & {0\;\%} & \cdots \\\cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots \\\cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots\end{pmatrix}$ $B_{out} = \begin{pmatrix}\ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\\ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\\ldots & {100\mspace{11mu}\%} & {100\mspace{11mu}\%} & {120\mspace{11mu}\%} & {50\;\%} & {{- 20}\;\%} & {0\;\%} & {0\;\%} & \cdots \\\cdots & {100\mspace{11mu}\%} & {100\mspace{11mu}\%} & {120\mspace{11mu}\%} & {50\;\%} & {{- 20}\;\%} & {0\;\%} & {0\;\%} & \cdots \\\cdots & {100\mspace{11mu}\%} & {100\mspace{11mu}\%} & {120\mspace{11mu}\%} & {50\;\%} & {{- 20}\;\%} & {0\;\%} & {0\;\%} & \cdots \\\cdots & {100\mspace{11mu}\%} & {100\mspace{11mu}\%} & {120\mspace{11mu}\%} & {50\;\%} & {{- 20}\;\%} & {0\;\%} & {0\;\%} & \cdots \\\cdots & {100\mspace{11mu}\%} & {100\mspace{11mu}\%} & {120\mspace{11mu}\%} & {50\;\%} & {{- 20}\;\%} & {0\;\%} & {0\;\%} & \cdots \\\cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots \\\cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots\end{pmatrix}$

The derivative at the edge is increased by 40%. The following exampleshows how a corner is enhanced after convolution by the same kernel.

$B_{i\; n} = \left( {\begin{matrix}\ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\\ldots & {100\mspace{11mu}\%} & {100\mspace{11mu}\%} & {100\mspace{11mu}\%} & {60\mspace{11mu}\%} & {0\;\%} & {0\;\%} & {0\;\%} & \ldots \\\ldots & {100\mspace{11mu}\%} & {100\mspace{11mu}\%} & {100\mspace{11mu}\%} & {60\;\%} & {0\;\%} & {0\;\%} & {0\;\%} & \cdots \\\cdots & {100\mspace{11mu}\%} & {100\mspace{11mu}\%} & {100\mspace{11mu}\%} & {60\;\%} & {0\;\%} & {0\;\%} & {0\;\%} & \cdots \\\cdots & {100\mspace{11mu}\%} & {100\mspace{11mu}\%} & {100\mspace{11mu}\%} & {60\;\%} & {0\;\%} & {0\;\%} & {0\;\%} & \cdots \\\cdots & {40\mspace{11mu}\%} & {40\mspace{11mu}\%} & {40\mspace{11mu}\%} & {24\;\%} & {0\;\%} & {0\;\%} & {0\;\%} & \cdots \\\cdots & {0\;\%} & {0\;\%} & {0\;\%} & {0\;\%} & {0\;\%} & {0\;\%} & {0\;\%} & \cdots \\\cdots & {0\;\%} & {0\;\%} & {0\;\%} & {0\;\%} & {0\;\%} & {0\;\%} & {0\;\%} & \cdots \\\cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots\end{matrix}.} \right)$ $B_{out} = \begin{pmatrix}\ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\\ldots & {100\mspace{11mu}\%} & {100\mspace{11mu}\%} & {116\;\%} & {68\;\%} & {{- 24}\;\%} & {0\;\%} & {0\;\%} & \ldots \\\ldots & {100\mspace{11mu}\%} & {100\mspace{11mu}\%} & {116\;\%} & {68\;\%} & {{- 24}\;\%} & {0\;\%} & {0\;\%} & \cdots \\\cdots & {100\mspace{11mu}\%} & {100\mspace{11mu}\%} & {116\%} & {68\%} & {{- 24}\;\%} & {0\;\%} & {0\;\%} & \cdots \\\cdots & {124\mspace{11mu}\%} & {124\mspace{11mu}\%} & {138\mspace{11mu}\%} & {81\;\%} & {{- 20}\;\%} & {0\;\%} & {0\;\%} & {\cdots.} \\\cdots & {32\mspace{11mu}\%} & {32\mspace{11mu}\%} & {39\mspace{11mu}\%} & {23\;\%} & {{- 11}\;\%} & {0\;\%} & {0\;\%} & \cdots \\\cdots & {{- 16}\mspace{11mu}\%} & {{- 16}\mspace{11mu}\%} & {{- 14}\mspace{11mu}\%} & {{- 9}\;\%} & {{- 2}\;\%} & {0\;\%} & {0\;\%} & \cdots \\\cdots & {0\;{\%.}} & {0\;\%} & {0\;\%} & {0\;{\%.}} & {0\;{\%.}} & {0\;{\%.}} & {0\;\%} & \cdots \\\cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots\end{pmatrix}$

A convolution with a derivative kernel enhances all edges, i.e. it doesa global edge enhancement. The off-grid filter is rule-based in thesense that it enhances only off-grid edges. The off-grid filter detectsthat the edge is interpolated and enhances it, while an edge that is notinterpolated is left unchanged. A simple condition for interpolation isthat the edge pixels have an intermediate value. The rule that onlyinterpolated edges are enhanced can be expressed as an IF-THEN-ELSE rulein the bitmap domain, but a more elegant implementation is by means ofmultiplication with a weight function that continuously varies between asmall magnitude in an on-grid position and a high magnitude in anoff-grid position.

Several embodiments of an off-grid correction filter are describedbelow. Two variations on the first embodiment are illustrated by FIGS.24 a-b. FIG. 24 a illustrates an off-grid filter implementation. B isthe bitmap from the rasterizer with values in the range 0-1. K is acoefficient array or kernel 3×5, 5×5 pixels or larger. W is a weightingbitmap used to weight the contribution to each entry in the bitmap B.Wn=4*(1−Bn)*Bn+max(4*(1−Bneighbors)*Bneighbors). An adjusted value ofB13 is computed as:B13filtered=B13+W13*(K7*B7+ . . . +K19*B19), whereW13=4*(1−B13)*B13+MAX(4*(1−B7)*B7, . . . , 4*(1−B12)*B12,4*1−B14)*B14, .. . , 4*(1−B19)*B19).

FIG. 24 b illustrates another off-grid filter. B is the bitmap from therasterizer with values in the range 0-1. G and F are derived bitmapsused for the filter. Gn=2(Bn−0.5). Fn=4(Bn−1)(Bn−0). K is a coefficientarray or kernel 3×5, 5×5 pixels or larger. An adjusted value of B13 iscomputed as:B13filtered=B13+K7*G7*F7*B7+ . . . +K19*G19*F19*B19.

The same or similar functions can be implemented in other ways, which isobvious for one skilled in the art.

The constants used in the edge enhancement and for the calculation ofthe “grayness” can be varied to produce as good results as possible fora variety of typical pattern elements, “use cases”. They can bedetermined manually by controlled experiments or by simulations usingcodes such as PROLYTH from KLA-Tencor or Solid-C from Sigma-C. In a moreelaborate setup the use cases can be programmed into an optimization jobusing one of the simulators above and non-linear optimization routines.

FIGS. 35 a-b illustrate another embodiment of an off-grid correctionfilter. This version of the off-grid filter operates duringrasterization on the area bitmap and detects and raises gray pixels andlowers dark pixel neighbours to negative black. The pixel values arechanged with two look-up tables, pre-computed before exposure, one forthe gray pixel and one for the dark pixel. FIG. 35 a, to the left,illustrates an uncompensated edge including a grey pixel P1, a darkpixel P2 and a light pixel. The uncompensated gray value on pixel P1,determines the compensated gray values P1* and P2*, according to:P1*=LUT1(P1) and P2*=LUT2(P1), where LUT1 and LUT2 are two differentlook-up tables. After compensation, in FIG. 35 b, the grey level ofcompensated grey pixel P1* has increased and the grey level ofcompensated dark pixel P2* has dropped below grey level 0.

In this embodiment, the LUTs are calculated with an infinite edge movingover one pixel in n steps, for instance, using the MATLAB linspacefunction on an equivalent. For each nominal edge position (correspondingto an area coverage), the position and Image Log Slope at a referencelevel is compared with when edge is on grid. A reference level isdetermined for pattern on grid. The LUTs are calculated iteratively.

Initial values for the LUTs are:LUT1(1:n,1)=linspace(0,1,n)LUT1(1:n,2)=linspace(0,1n)LUT2(1:n,1)=lispace(0,1,n)LUT2(1:n,2)=a*x^2−a*x, x=linspace(0,1,n),

-   -   where a=0.217*4, i.e maximum negative black *4, or something        else

The LUTs are applied to pixel P1 and P2, according to:P1*=LUT1(P1,2)P2*=LUT2(P1,2)

An aerial image is then calculated. Correction terms, at each n steps,are calculated for position and ILS as:Corr_pos=nominal_position/real_positionCorr_ILS=ILS_reference/ILS_real

Either LUT1 or LUT2 is updated, depending on if position or ILS isoptimizedLUT1_new(P1,2)=LUT1(P1,2)*Corr_posLUT2_new(P1,2)=LUT2(P1,2)*Corr_ILS

If one converge criteria is fulfilled, repeat from applying the LUT topixels P1 and P2 and optimize with respect to the other until bothcriteria are fulfilled.

FIG. 36 illustrates resulting LUT functions. LUT1 for P1 is the top linein the graph. LUT2, for P2, almost reaches down to maximum negativeblack amplitude attainable by a tilting micromirror.

Calculations of the improvement due to this embodiment of the off-gridfilter are illustrated in FIGS. 37 a-b, 38 a-b and 39 a-b. Some of theparameters used to calculate these results were: 90 nm dense L/S;annular illumination 0.7/0.9; 2 nm mesh grid; 30 nm pixel size; 13 pupilmesh points; and NA 0.92925925925926.

FIG. 37 a-b illustrates placement error versus grid shift. In FIG. 37 a,the smallest placement error of zero corresponds to a grid shift of 0,15 or 30 nm, using an illumination table LUT. With the off-gridcorrection filter of this embodiment, there is very little placementerror, regardless of the grid shift, through the range of 0 to 30 nm. InFIG. 38 a-b, the contrast attained between opposing sides of theintended boundary between dark and light is again graphed against gridshift for the illumination table LUT (38 a) and the off-grid correctionfilter of this embodiment (38 b). Finally, normalized image log slope isplotted against grid shift for the illumination table LUT (39 a) and theoff-grid correction filter of this embodiment (39 b). Those of skill inthe art will understand that normalized image log slope is normalized tofeature size and tends to be proportional to exposure latitude. Varyingthe parameters to 60 nm dense L/S and 15 pupil mesh points changes theshapes of some of the curves in these figures, but generally confirmsthe performance of this embodiment of the off-grid filter.

Operation of another embodiment is illustrated in FIGS. 40 a-b. Thisversion of the off-grid filter also operates directly on the area bitmapand replaces the illimunation table LUT. During the operation, edges aredetected, and the edge pixel and the two neighbouring pixels aremodified. The pixel values are changed with three look-up tables, onefor each pixel. The look-up tables are pre-computed before exposure. InFIG. 40 a-b, P1 (grey pixel), P2 (dark pixel), and P3 (light pixel) aregraphed against their area bitmap gray levels, i.e. area coverage. Theuncompensated gray value on pixel 1, P1, determines the compensated grayvalues P1*, P2, and P3*, according to:P1*=LUT1(P1)P2*=LUT2(P1)P3*=LUT2(P1)

-   -   where LUT1, LUT2, and LUT3 are three different look-up tables.

The LUTs are calculated by substantially minimizing the difference inthe Fourier transform (FT) from the SLM and a perfect binary orphase-shifting mask over the projection optics pupil.

The edge offset correction filter, which may substantially minimize thedifference in the Fourier transform from projecting radiation from thealigned pixels of the SLM and a perfect binary mask or phase shiftingmask over the projection optics pupil may be performed using one two,three or more pixels.

FIG. 41 a, to the left, illustrates an SLM with a feature with a widthw*(1+gl), were w is the pixel width and gl is in the range [0, 1]. Thepixels are modeled with an amplitude transmission that can have negativevalues. a, b, and c are parameters used to minimize the diffractionpattern difference compared to the ideal case. The complementary FIG. 41b illustrates an ideal pattern from a binary mask. The feature has thesame width as in the SLM case, w*(1+gl). The real and imaginary part ofthe difference in the FT, FT_SLM(fx,a,b,c,gl)−FT_ideal(fx,gl), is foreach value of gl, minimized for all fx in the range[−NA(1+sigma)/lambda, NA(1+sigma)/lambda]. NA is the numerical apertureof the projection optics and sigma is the degree of coherence in theillumination.

FT_SLM = w * sin  c(w * fx) * (1 + a + (g 1 + b) * exp (−𝕚 * 2 * p * w * fx) + c * exp (−𝕚 * 4 * p * w * fx))FT_ideal = w * sin  c(w * fx) + g 1 * w * sin  c(g 1 * w * fx) * exp (−𝕚 * p * w * fx(1 + g 1))$\begin{matrix}{{F\_ min} = {\left( {{FT\_ SLM} - {FT\_ ideal}} \right)/\left( {w*\sin\;{c\left( {w*{fx}} \right)}} \right.}} \\{= {a + {b*{\exp\left( {{- {\mathbb{i}}}*2*p*w*{fx}} \right)}} + {c*{\exp\left( {{- {\mathbb{i}}}*4*p*w*{fx}} \right)}} +}} \\{{g\; 1*{\exp\left( {{- {\mathbb{i}}}*2*p*w*{fx}} \right)}} -} \\{g\; 1*\sin\;{{c\left( {g\; 1*w*{fx}} \right)}/\sin}\;{c\left( {w*{fx}} \right)}*{\exp\left( {{- {\mathbb{i}}}*p*w*{{fx}\left( {1 + {g\; 1}} \right)}} \right)}}\end{matrix}$

-   -   The equation system above can be re-written in a matrix form,        A*x=h. The over-determined linear equation system A(fx)* [a, b,        c]=h(fx,gl), is solved in a least square sense.

In FIG. 42, the resulting calculations are graphed for lambda=193 nm,w=30 nm, NA=0.93, sigma=0.96. The top line depicts LUT3=a. The bottomline depicts LUT2=c. The middle line depicts LUT1=b.

In FIG. 43, application of this embodiment of the grid filter has beenperformed on dense lines and spaces, with half pitch 60 nm. The resultis a smaller CD range, a smaller PE range, higher contrast, a smallercontrast range, a higher NILS and a smaller NILS range than with theillumination table LUT.

This embodiment of the grid filter can be extended to include not onlybinary masks, but also phase-shifting masks, including weak and strongphase-shifting (chromeless phase lithography (CPL)). FIGS. 44 and 45illustrates in the same way as FIGS. 41 and 42, an SLM and an idealpattern from a reference reticle both with a feature with a widthw*(1+gl), where w is the pixel width, gl is in the range [0,1], and gldis equal to gl*(1−d)+d, i.e. gld is equal to gl scaled to the range [d,1]. In this case, the transmission in the area outside of the feature isnot zero, but instead the amplitude has a magnitude d, which can haveany value from −1 up to any value lower than the transmission in thebright areas. Hence, it can be zero as in a binary mask, between −1 andzero as in phase-shifting masks, or −1 as in CPL. The correspondingequations describing the Fourier transforms of the SLM, the perfectphase-shifting reticle, and the difference to be minimized are in thiscase:

FT_SLM = w * sin  c(w * fx) * (1 + a − d + (g 1 d + b − d) * exp (−𝕚 * 2 * p * w * fx) + c * exp (−𝕚 * 4 * p * w * fx)) + d * δ(fx)FT_ideal = (1 − d) * w * sin  c(w * fx) + (1 − d) * w * sin  c(g 1 * w * fx) * exp (−𝕚 * p * w * fx(1 + g 1)) + d * δ(fx)$\begin{matrix}{{F\_ min} = {\left( {{FT\_ SLM} - {FT\_ ideal}} \right)/\left( {w*\sin\;{c\left( {w*{fx}} \right)}} \right.}} \\{= {a + {b*{\exp\left( {{- {\mathbb{i}}}*2*p*w*{fx}} \right)}} + {c*{\exp\left( {{- {\mathbb{i}}}*4*p*w*{fx}} \right)}} +}} \\{{\left( {{g\; 1d} - d} \right)*{\exp\left( {{- {\mathbb{i}}}*2*p*w*{fx}} \right)}} -} \\{\left( {1 - d} \right)*g\; 1*\sin\;{{c\left( {g\; 1*w*{fx}} \right)}/\sin}\;{c\left( {w*{fx}} \right)}*} \\{{\exp\left( {{- {\mathbb{i}}}*p*w*{{fx}\left( {1 + {g\; 1}} \right)}} \right)},}\end{matrix}$where δ(fx) is the dirac delta function.

As mentioned previously, the equations above apply to binary, weak andstrong phase-shifting (CPL). When the SLM and grid filter is used tomimic the performance of alternating aperture phase-shifting masks(AAPSM), the equations above cannot be applied directly. For AAPSM, thebright areas in the mask with opposite phase must be treated separatelyand the resulting pixel values are added together. The areas with zerophase can simply, together with the surrounding dark areas, be treatedas from a binary mask and the corresponding settings should be used. Thebright areas with 180 degree phase can, together with the surroundingdark areas, in the same way be treated as from a binary mask, but simplywith a negative transmission.

In FIG. 46, the resulting calculations are graphed for lambda=193 nm,w=30 nm, NA=0.93, sigma=0.96, and d=−√(0.06)=−0.245. The value of dcorresponds to a 6% attenuated phase-shift mask. The top line depictsLUT3=a. The bottom line depicts LUT2=c. The middle line depicts LUT1=b.Note that the value of the uncompensated edge pixel, P1, is in the range[d, 1]. FIG. 9 a-d shows simulated performance of a manually fittedenhanced space (clear line). The vector data has one edge 912 on gridand one off grid 914. If it is rasterized without edge enhancements theresult is an aerial image where the on-grid edge has higher acuity thanthe off-grid one. If the dose is varied the width of the trench varies,but the two edges 991, 992 move differently with dose. This is seen as amovement of the center of the space with dose. The diagram 9 d shows themovement with dose of the center of the space without 970 and with 980the off-grid filter. It is seen that with the off-grid edge enhanced thecenter of the space is stable over a very large dose interval. This isan alternative way to describe that the left and right edges in theaerial image are closely identical. A pixel within the feature 940 isset to a higher exposure value, here 116% compared to the rest of thepixels within the feature, which are set to 100%. A pixel 950 outsidethe feature is set to a negative black value, i.e., a negative complexamplitude reflectivity. The rest of the outside feature pixels are setto 0%.

The example in FIG. 9 b has a minimum negative value of −√{square rootover (0.72%)}=−0.085. It was shown above that the square mirrors couldcreate value of −0.25 or even below. Therefore there is room for furtheredge enhancement using negative complex amplitude even after some of thedynamic range of the mirrors has been used for the off-grid filter. Theoperation can conceptually be expressed as a convolution with two parts.

B_(out)=B_(in){circle around (x)}(D_(global)+g*D_(off-grid)), whereDglobal is the edge enhancement kernel for global edge enhancement,Doff-grid the kernel for removing the difference between off-grid andon-grid edges and g is the “grayness”, the weight function thatdetermines the application of Doff-grid.

In a further improvement the convolution kernel, or more generally thedigital filter, has slightly different properties in the x and ydirections to correct for inherent differences in edge acuity between xand y.

In order to print a true image of the input data the pixel values cannotbe a linear representation of the overlap between the pixel area and thefeature. There has to be a non-linear transformation between overlaparea and pixel value. Regardless if the representation of the pixelvalues is chosen to be tilt angle, actuator voltage, complex amplitudereflectivity R or |R2| a non-linear pixel-by-pixel transformation isneeded: V=I(A)*A where V is the pixel value, A the area overlap from 0to 100%, and I(A) is the illumination table. The illumination table I(A)describes the non-linearity of the system that arises from the partialcoherence over the modulating element (mirror). The shape of thefunction depends on the pixel size relative to the optical resolution,the angular spread of the illuminating light, the used dynamic range ofthe SLM, and the relative dose (dose/dose-to-clear).

The illumination function can be determined empirically or throughoptical simulation. In either case the printing conditions such as NA,illuminator setting, pixel size, SLM contrast, and dose are fixed. Alarge feature is printed from vector data with the placement of one edgeversus the grid varying, either in resist or virtually in a lithographysimulator. The pixel value is a predetermined function of the featureoverlap with the pixel area, possibly with a non-uniform weight functionover the pixel area The predetermined function can for example be alinear function.

The feature is printed for different edge placements and the placementof the printed edge is measured, either by a metrology system such asLeica IPRO or by numerical analysis of the simulated images. Themeasurement gives a non-linear function for placement vs. data. Thisnon-linear function is used to compute the illumination table. Theprocedure can be repeated iteratively in order to arrive at a stable andaccurate illumination table. This illumination table makes the printerprint true to data for large features with the used printing conditions.

A preferred embodiment of the invention has the following order ofconversions: see FIG. 8 a

1. Flatten the hierarchical input database, 2. Rasterize all featuresand compute the overlap area of feature elements for every bitmap pixel(possibly using a non-uniform area sampling function per pixel)producing a so called area bitmap, 3. Make pattern corrections(preferably in real time) including edge enhancement and off-gridenhancement as well as special enhancement of corners and smallfeatures, producing a corrected area bitmap, 4. Multiply the correctedbitmap by the illumination function producing what is currently calledan intensity bitmap, 5. Make a table look-up conversion of the intensitybitmap, the lookup table representing the properties of individualmodulator elements or mirrors, producing a DAC value bitmap

A slightly more complex conversion sequence gives more control of thenon-linearities of the rasterizing and partially coherent imaging: seeFIG. 8 b 1. Flatten the hierarchical input database, 2. Rasterize allfeatures and compute the overlap area of feature elements for everybitmap pixel (possibly using a non-uniform area sampling function perpixel) producing a so called area bitmap, 2b Multiply the area bitmap bya first illumination function, 3. Make pattern corrections (preferablyin real time) including edge enhancement and off-grid enhancement aswell as special enhancement of corners and small features, producing acorrected area bitmap, 4. Multiply the corrected bitmap by a secondillumination function producing what is currently called an intensitybitmap, 5. Make a table look-up conversion of the intensity bitmap, thelookup table representing the properties of individual modulatorelements or mirrors, producing a DAC value bitmap

In a third embodiment, see FIG. 8 c the pattern is divided into two(possibly three or more) partial patterns, e.g. one containing morehigh-frequency information and another one containing more low-frequencyinformation. The partial patterns are converted with differentparameters before they are combined to drive the SLM. The decompositionis suitably implemented as different bitmap filters such as theconvolutions described above. High and low frequency filtering of imagesis well known in the art of digital image processing and many methodsand detailed implementations can be devised by a person skilled in theart.

In all embodiments the illumination function can be folded into themirror look-up table. The mirror LUT (Look Up Table) must then bechanged depending on the angular spread of the illumination and thedose.

The illumination table makes the CD independent of the pixel grid, atleast for large features. But the illumination does not make the aerialimage acuity constant through grid. Features at the resolution limittend to disappear, and features placed at grid positions where theacuity is compromised by the rasterization disappear first. Thereforeline width CD is not stable through grid at the resolution limit.

The off-grid enhancement makes the image of on-gid and off grididentical. This makes all printing properties more stable, e.g. forvarying dose. But the main benefit is that features at the resolutionlimit become much more stable. In this way the useful resolution isimproved.

The global edge enhancement also increases the useful resolution. Itincreases the contrast of thin lines by extending the dynamic range ofthe SLM modulator elements. Edges are made crisper. Since small featureshave the edges close together they get a double boost.

The edge enhancement method is exemplified by embodiments based ontilting micromirror SLMs. It is obvious that the same methods can beapplied to other SLMs or modulator arrays, in particular to SLMs havingthe ability to create negative complex amplitude, such asmicromechanical mirrors having pistoning or combined pistoning andtilting action or LCD SLMs.

Line ends are also improved, partly because all edges are made crisper,but also because the convolution with a derivating kernel enhances thecontrast of line ends. Corners are likewise enhanced, although not asmuch as line ends. With properly chosen parameters line end shorteningand CD linearity failures of lines and contacts can be largelycounteracted. If the global enhancement is implemented as a convolutionwith a derivating kernel the size of the kernel and the coefficients init can be used to determine the magnitude and detailed properties of theenhancement. The complex amplitude of the square mirror and how itvaries with the tilt angle is calculated as described above. It isinfluenced by the shape of the mirror. Other shapes give othercharacteristics and shown in FIG. 14-23, 25-31.

One can make a distinction between shapes that are area filling or not.For instance FIG. 10 a, 18 a, 19 a are surface filling. FIG. 14 a-23 a,25 a-31 a shows that many perfectly viable mirror shapes have radicallydifferent complex amplitude reflectivity. By selecting a differentmirror shape one can get access to large amounts of negative R. Some ofthe shapes, like the H shape in FIG. 22 a, can provide a symmetricalpositive and negative R.

FIG. 11 a depicts mirror configurations in a spatial light modulator,which may be used in order to achieve any desired pattern with improvedimage quality. Mirror 1110 and 1120 have their tilting axis alongsymmetry line 1130. Mirror 1110 have outer areas with phase 0 and innerarea with phase 180. Mirror 1120 are reversed relative to mirror 1110,i.e., outer areas have phase 180 and inner area has phase 0. Mirror 1110and 1120 are arranged in a chess board manner, i.e., mirror 1110 issurrounded by four 1120 mirrors and mirror 1120 is surrounded by four1110 mirrors. FIG. 11 b illustrates the real part of the complexamplitude reflectivity as function of a degree of tilting of the mirror.As can be seen from FIG. 11 b, mirror element 1110 goes from +1 to −1 asthe mirror is tilted and mirror element 1120 goes from −1 to +1 as themirror is tilted. With mirror characteristics as depicted in FIGS. 11 aand 11 b patterns as depicted in FIG. 12 a-12 e can easily be achieved.FIG. 12 a illustrates a pattern with uniform phase 0. Only mirrors 1120,denoted in FIG. 12 a with phase 180 and an arrow, are tilted. Thedirection of said arrow indicates the direction of tilting. Every secondmirror is tilted in a reversed direction. However mirrors may all betilted in the same direction.

FIG. 12 b illustrates a pattern with uniform phase 180. In FIG. 12 b areonly the mirrors 1110 tilted, denoted in FIG. 12 b with phase 0 and anarrow. Here again a direction of said arrow indicates the direction oftilting said mirror.

FIG. 12 c-e depict patterns with uniform dark. In FIG. 12 c none of themirrors are tilted. In FIG. 12 d all mirrors are tilted. In FIG. 12 eall mirrors are partially tilted. In FIG. 12 c-e the direction of saidarrow indicates the tilting direction of the mirror. Controlling thecharacteristics of the mirrors with the shape leads to inflexibledesigns where a modest change in properties may necessitate a change inlayout affecting both the CMOS underneath the MEMS and the rasterizingalgorithms. It is possible to change the apparent shape of the mirrorsby covering the unwanted parts of the mirrors with a non-reflectinglayer, e.g. a dark metal like zirconium, an anti-reflection coating likea deposited metal oxide or other dielectric film as is well known in theart. A practical way of controlling the characteristics of the mirrorsis by structures on the top surface of the mirror. One advantage is thatit may use the same material as the rest of the mirror, another that,whatever material is used there is no requirement to reduce thereflectivity, since the effect of the surface structures is created bydivision-of-wavefront destructive interference and light scattering. Theareas that are intended to be non-reflected can be patterned bystructures that create destructive interference in the speculardirection. An example is a checkerboard of squares with a step height oflambda over 4 (lambda over 2 in the reflected beam). It has been foundthat with partially coherent illumination the structures can be fairlylarge. FIG. 12 shows a number of possible designs and correspondingproperties.

FIG. 13 a-d illustrates the correspondence between Masks or reticles andan SLM having similar properties. A leftmost illustration in FIG. 13 adepicts a binary mask. The binary mask has a part, which is covered witha chrome layer. Said chrome layer is opaque. Next to the chrome layersaid mask is clear, defining a fully transmissive part of said mask. Arightmost illustration depicts an SLM with corresponding properties assaid binary mask. The chrome part in said binary mask corresponds to acomplex amplitude reflectivity A=0 and the clear part in said binarymask corresponds to a complex amplitude reflectivity A=1.

A leftmost illustration in FIG. 13 b depicts an attenuating phase shiftmask. The attenuating phase shift mask has a part, which is covered witha partly transmissive layer. Next to the partly transmissive layer saidmask is clear, defining a fully transmissive part of said mask. Arightmost illustration depicts an SLM with corresponding properties assaid attenuating phase shift mask. The partly transmissive layer in saidattenuating phase shift mask corresponds to a complex amplitudereflectivity in the range of −1<A<0 and the clear part in said binarymask corresponds to a complex amplitude reflectivity A=1.

A leftmost illustration in FIG. 13 c depicts an alternating phase shiftmask. The alternating phase shift mask has a first part, which iscovered with a chrome layer. Said chrome layer is opaque. At one side ofthe chrome layer said mask is clear, defining a fully transmissive partof said mask. At another side of said chrome layer said mask is shiftedin phase relative said chrome layer and said clear part. A rightmostillustration depicts an SLM with corresponding properties as saidalternating phase shift mask. The chrome part in said alternating phaseshift mask corresponds to a complex amplitude reflectivity A=0. Theclear part in said alternating phase shift mask corresponds to a complexamplitude reflectivity A=1. The shifted part in said alternating phaseshift mask corresponds to a complex amplitude reflectivity A=−1.

A leftmost illustration in FIG. 13 d depicts a CPL (Chrome-less PhaseLithography) mask. The CPL mask has a part, which is covered with ashifted layer. Said shifted layer is clear and fully transmissive. Nextto the shifted layer said mask is clear, defining a fully transmissivepart of said mask. The shifted part has its surface higher or lower thansaid clear part. The rightmost illustration depicts an SLM withcorresponding properties as said CPL mask. The shifted part in said CPLmask corresponds to a complex amplitude reflectivity A=−1 and the clearpart in said CPL mask corresponds to a complex amplitude reflectivityA=1.

The different parts in FIG. 13 a-d comprises typically a plurality ofpixel elements, i.e., in the SLM case said areas are represented by aplurality of SLM pixels, the number depending on the size of the featureto be patterned.

FIG. 14-31 illustrates different mirror configurations and correspondingcomplex amplitude trajectory, complex amplitude reflectivity graph andexposure graph as a function of phase at an edge of the mirror.

FIG. 14 a illustrates a square shaped mirror 145 capable to be tilted athinges 147, 148 defining a tilting axis. FIG. 14 b illustrates thecomplex trajectory for said square shaped mirror. As can be seen fromFIG. 14 b an imaginary part of the complex amplitude is almost zeroindicating that the mirror element is nearly symmetrical. Symmetricalmirror elements have the imaginary part equal to zero. FIG. 14 cillustrates the reflection and exposure as functions of a phase of themirror element at an edge of the same. The reflection is the real partof the complex amplitude reflectivity. The exposure is the square of thereal part of the complex amplitude reflectivity. In the same FIG. 14 c amagnified portion of the exposure is illustrated. A square mirror has arelatively low level of negative real part of the complex amplitude,therefore full phase shifting cannot be obtained.

FIG. 15 a illustrates another configuration of a mirror. In thisembodiment the hinges 157, 158 are attached to the mirror 155 closer tothe center compared to the mirror in FIG. 14 a. This embodiment has lessreflecting area compared to the mirror illustrated in FIG. 14 a,especially it has less reflecting area close to the tilting axis definedby the hinges 157, 158. This will affect the minimum value of thecomplex amplitude as illustrated in FIGS. 15 b and 15 c, in that thereal part has a minimum, which is more negative than the embodimentillustrated in FIG. 14 a.

FIG. 16 a illustrates another configuration of a mirror. In thisembodiment the hinges 167, 168 are attached to the mirror 165 evencloser to the center compared to FIG. 14 a and FIG. 15 a. Thisembodiment has less reflecting area compared to the mirror illustratedin FIG. 14 a and 15 a, especially it has less reflecting area close tothe tilting axis defined by the hinges 167, 168. This will affect theminimum value of the complex amplitude as illustrated in FIGS. 16 b and16 c, in that the real part has a minimum, which is more negative thanthe embodiment illustrated in FIG. 14 a and FIG. 15 a.

FIG. 17 a illustrates yet another configuration of a mirror. In thisembodiment the hinges 177, 178 are attached to two diagonally displacedcorners of the mirror 175. The illustrated embodiment has no negativecomplex amplitude, neither real nor imaginary.

FIG. 18 a illustrates still another configuration of a mirror 185. Tosaid mirror 185 are attached two hinges 187, 188, defining a tiltingaxis. This configuration has two sides, which are zigzag-formed, whereone is the inverse of the other. This configuration, as well as thepreviously illustrated ones, is perfectly suitable to be stitchedtogether in a one- or two-dimensional array of micromirrors, such as ina spatial light modulator. The complex amplitude trajectory isillustrated in FIG. 18 b, which indicates that this embodiment has aslightly negative complex amplitude. FIG. 18 c illustrates the exposureand reflection for the configuration in FIG. 18 a.

FIG. 19 a illustrates still another configuration of a mirror 195. Tosaid mirror 195 are attached two hinges 197, 198, defining a tiltingaxis. This embodiment has also two sides where one is the inverse of theother one. This configuration is suitable to be stitched together in theone or two-dimensional array of mirrors. As can be seen in FIGS. 19 band 19 c this embodiment has less negative complex amplitude compared tothe configuration illustrated in FIG. 18 a.

FIG. 20 a illustrates still another configuration of a mirror 205. Thisembodiment differs to the one illustrated in FIG. 19 a in that areflecting area is slightly less than the embodiment illustrated in FIG.19 a. Areas are cut off around an attachment position of hinges 207,208, which is not the case in FIG. 19 a. As can be seen in FIG. 20 b, 20c, this embodiment has slightly more negative complex amplitude than theconfiguration in FIG. 19 a.

FIG. 21 a illustrates still another mirror configuration. In thisconfiguration hinges 217, 218 define a tilting axis. Here the mirrorarea is much less close to the tilting axis compared to further away,which will affect the complex amplitude of the mirror, see FIG. 21 b and21 c. As the mirror element is almost symmetrical there is no imaginarypart of the complex amplitude present. The real part of the complexamplitude is more negative than all previously illustrated embodimentsabove.

FIG. 22 a illustrates still another mirror configuration. Hinges 227 and228 define a tilting axis as previous. In this embodiment there isalmost no reflecting area close to the tilting axis. Nearly allreflecting areas are at a distance from the tilting axis. This willincrease the negative complex amplitude even more compared to theembodiment illustrated in FIG. 21 a. This configuration is also suitableto be arranged in a one or two-dimensional array of mirror elements.This is illustrated in FIG. 22 d.

FIG. 23 illustrates still another mirror configuration 235. Hinges areattached to support structures 237, 238. The hinge are may be coveredwith an anti-reflective coating in order not to reflect any radiation ata predetermined wavelength, said hinges are hidden for said reason nFIG. 23 a. Also hidden is a connecting element connecting reflectingareas 236, 239. This configuration exhibit exceptional complex amplitudevalues as indicated in FIG. 23 b and FIG. 23 c. The real part of thecomplex amplitude goes from +1 to −1 and there is no imaginary part ofthe complex amplitude.

FIG. 25 a illustrates still another embodiment of a mirror configuration255. This embodiment differs to the one illustrated in FIG. 15 a in thatsome corner areas 251, 252, 253, 254 of the mirror are out of phaserelative the rest of the mirror. Preferably said corner areas affect areflected wavelength so that said reflected wavelength from said cornerareas are 180 degrees out of phase relative to the other mirror areas.As illustrated in FIG. 25 b, 25 c, the complex amplitude will decreasecompared to the embodiment in FIG. 15 a.

FIG. 26 a illustrates still another mirror configuration 265. In thisconfiguration there are two areas 261, 262 which are out of phaserelative to the rest of the mirror. Preferably said areas affect areflected wavelength so that said reflected wavelength from said areasare 180 degrees out of phase relative to the other mirror areas. Thisembodiment will affect the complex amplitude, see FIG. 26 b, 26 c,slightly different compared to the embodiment illustrated in FIG. 25 a.

FIG. 27 a illustrates yet another embodiment of a mirror configuration275. Here are out of phase areas 271, 272 larger than the out of phaseareas in FIG. 26 a. This will affect the position of the local maximumand minimum positions of the reflection, see FIG. 27 c compared withFIG. 26 c, as well as this embodiment give a more negative complexamplitude than the embodiment in FIG. 26 a.

FIG. 28 a illustrates still another mirror configuration 285. Here thecentral part of the mirror is covered with an area 281, which area is180 degrees out of phase relative the rest of the mirror. Thisembodiment will cause the complex amplitude to go from +1 to −1, seeFIG. 28 b, 28 c.

FIG. 29 a illustrates still another mirror configuration 295. Here thecentral part of the mirror 295 is covered with an area 180 degrees outof phase relative the rest of the mirror. The area is slightlydifferently shaped compared to the one in FIG. 28 a, resulting inslightly different complex amplitude values, see FIG. 29 a, 29 b.

FIG. 30 a illustrates still another mirror configuration 305 having acentral part covered with an area 180 degrees out of phase relative tothe rest of the mirror. In the embodiments illustrated in FIG. 25 a-30 athe area 180 degrees out of phase relative to the other part of themirror apply to reflected light/electromagnetic radiation.

FIG. 31 a illustrates still another mirror configuration 315. Here thereare two areas, which are out of phase for reflectedlight/electromagnetic radiation relative the rest of the mirror. A firstarea 311 is −90 degrees out of phase relative to the non-hatched mirrorareas. A second area 312 is +90 degrees out of phase relative thenon-hatched parts of the mirror. This embodiment will give an extendeddeflection range giving 0 reflection, see FIG. 31 c. As can be seen fromFIG. 31 b this mirror configuration has no imaginary part.

FIG. 31 a has areas (hatched in figure) with different heights thanlambda over four. Such structures can be used to further modify thepixel characteristics. The example in FIG. 31 a gives an R maximum at asmall tilt and a plateau at R=0. This mirror is easier to calibrateaccurately than the other mirrors shown.

There are at least three interesting cases of ranges of complexamplitude reflectivity cases. The first one relates to full phaseshifting capability, which means that the complex amplitude reflectivitygoes from +1 to −1, a plurality of mirror configurations having suchcharacteristic has been disclosed above.

The second one relates to attenuated phase shift masks, which means thatthe complex amplitude goes from +1 to −0,245.

The third one relates to an ordinary chrome mask, which means that thecomplex amplitude goes from +1 to 0.

A suitable mirror design gives a relative flat graph for the complexamplitude as a function of mirror tilt angle or reflected light at theedge of the mirror. Such mirror design will not be so sensitive tochanges in tilt angle for the desired gray-value of the mirror element.

When the complex amplitude is specified in the range −1 to 1 it impliesthat the amplitude is normalized, so that the highest amplitude that isused is normalized to +1.00. The same holds for complex amplitudereflection. Exceptions to this normalization are where it is obviousfrom the context that an actual value or a value normalized to an idealspecular reflecting surface is used.

These values are the same as those used in Levinson-type PSM,chrome-less phase lithography (CPL), and other so called strong PSMs. Bydriving the SLM to these values the same resolution and process latitudegains can be made as in wafer lithography using strong PSMs. Figure XXshows haw the Re(A) can be controlled to act as a number of commonlyused types of phase-shifting masks.

The H shape is also surface filling, but gives a pattern that is notoptimal for rasterizing. An equivalent mirror shape can be created froma square mirror place by reduction of the mirror reflectivity on someareas. The reflectivity can be reduced by coatings of a low-reflectancematerial or by structuring the surface to create destructiveinterference or light scattering away from the projection optics. Theillumination with the small angular spread used makes it possible to userather large surface structures.

In the description above negative values of R have been used for edgeenhancement and correction of grid and x-y artifacts. It is alsopossible to use the SLM as a strong phase-shifting mask (PSMs) as knownin lithography. The pixels in 7d and 8a-c can produce R values of 1.00,0.00, and −1.00 (after scaling by an increase of dose). These values arethe same as those used in Levinson-type PSM, chrome-less phaselithography (CPL), and other so called strong PSMs. By driving the SLMto these values the same resolution and process latitude gains can bemade as in wafer lithography using strong PSMs.

In addition the SLM also has intermediate values not present in commonlyused masks. These are used for placement of edges in a fine addressgrid. They can also be used for phase-shifting lithography equivalent to“high transmission PSMs” and “tri-tone masks” known in the art e.g. forprinting of dense contacts.

If there is a small asymmetry between R=1.00 and −1.00 it givesevery-second-line artifacts in the printed pattern. A remedy is shown inFIG. 11 b. The pixels form a checkerboard pattern where every secondmirror is displaced by 180 degrees, i.e. they move from −180 to +180degrees instead of the normal +180 to −180.

A strongly phase-shifting reticle normally have areas with three complexamplitudes A=+1.00, 0.00, and −1.00. Although they can be described witha single parameter they are usually defined in two binary (having areasof two kinds) mask data files: one file for dark and one file for thoseareas that are shifted, i.e. 180 degree phase. The shifter features areusually printed with an overlap of the chrome so that the chrome datadetermines the dimension in the mask.

An embodiment of an SLM printer using phase-shifting SLMs follows thescheme above. It rasterizes two binary (two-valued) input files andcombines them in a Boolean operation to create the multi-valued SLMbitmap data. Each binary set of data can have its own set of bitmapoperations, such as CD bias and edge enhancement. This preserves thehighest degree of transparency between mask and maskless pattern datafiles.

In another embodiment the rasterizer reads a file containing at leasttwo types of areas and a background, e.g. clear and shifted areas in adark background and rasterizes them directly to a multivalued bitmap.This has the advantage of creating immediately interpolated edges forall types of feature boundaries: clear to dark, shifted to dark, andclear to shifted. It is also more suitable for working directly from thedesign database without the intermediate step of mask data tape-out. Therelative benefits of the first and second type of rasterization dependon the application and a preferred embodiment can use either scheme.

While the present invention is disclosed by reference to the preferredembodiments and examples detailed above, it is understood that theseexamples are intended in an illustrative rather than in a limitingsense. It is contemplated that modifications and combinations willreadily occur to those skilled in the art, which modifications andcombinations will be within the spirit of the invention and the scope ofthe following claims.

1. A method of preparing fine patterns to be printed with an SLM,comprising the actions of: rasterizing an input pattern to a grayscalebitmap, applying an edge offset correction filter to at least twoaligned pixels, including at least one pixel having a grey value and alight value pixel or a dark value pixel, wherein operation of the edgeoffset correction filter depends at least in part on the grey value andapplication of the edge offset correction filter increases a differencein illumination of at least one area element adjacent to an edge of thefeature, located either on the dark side and/or one on the light side ofthe edge; and projecting radiation from the aligned pixels of the SLMthrough a Fourier filter onto an object plane.
 2. The method accordingto claim 1, wherein said light value corresponds to a value used toproject a white pixel when the white pixel is surrounded by other whitepixels.
 3. The method according to claim 1, wherein said dark valuecorresponds to a value used to project a black pixel when the blackpixel is surrounded by other black pixels.
 4. The method according toclaim 1, wherein application of the edge offset correction filter to thedark value pixel results in the dark value pixel having a negativeamplitude.
 5. The method according to claim 1, wherein application ofthe edge offset correction filter to the light value pixel results inthe light value pixel having a lighter amplitude than used to project awhite pixel when the white pixel is surrounded by other white pixels. 6.The method according to claim 1, wherein the edge offset correctionfilter, for at least some values of grey, is not symmetrical inlightening the light value and darkening the dark value.
 7. The methodaccording to claim 1, wherein the edge offset correction filter, for atleast some values of grey, also changes the grey value.
 8. The methodaccording to claim 1, wherein the edge offset correction filter is arule-based filter.
 9. A method of preparing fine patterns to be printedwith an SLM, comprising the actions of rasterizing an input pattern to agrayscale bitmap, applying an edge offset correction filter to at leasttwo aligned pixels, including at least one pixel having a grey value anda light value pixel or a dark value pixel, wherein operation of the edgeoffset correction filter depends at least in part on the grey value andapplication of the edge offset correction filter is changing the darkvalue pixel to a more negative amplitude and adjusts the grey value ofthe grey value pixel; and projecting radiation from the aligned pixelsof the SLM through a Fourier filter onto an object plane.
 10. A methodof preparing fine patterns to be printed with an SLM illuminated bypartially coherent light, comprising the actions of: rasterizing aninput pattern to a grayscale bitmap, applying an edge offset correctionfilter to at least three aligned pixels, including at least one pixelhaving a grey value and having on opposing sides a light value pixel anda dark value pixel, wherein operation of the edge offset correctionfilter depends at least in part on the grey value and application of theedge offset correction filter increases a difference between a complexamplitude of the light value pixel and the dark value pixel; andprojecting radiation from the aligned pixels of the SLM through a Fowierfilter onto an object plane.
 11. The method according to claim 10,wherein said light value corresponds to a value used, to project a whitepixel when the white pixel is surrounded by other white pixels.
 12. Themethod according to claim 10, wherein said dark value corresponds to avalue used to project a black pixel when the black pixel is surroundedby other black pixels.
 13. The method according to claim 10, whereinapplication of the edge offset correction filter to the dark value pixelresults in the dark value pixel having a negative amplitude.
 14. Themethod according to claim 10, wherein application of the edge offsetcorrection filter to the light value pixel results in the light valuepixel having a lighter amplitude than used to project a white pixel whenthe white pixel is surrounded by other white pixels.
 15. The methodaccording to claim 10, wherein the edge offset correction filter, for atleast some values of grey, is not symmetrical in lightening the lightvalue and darkening the dark value.
 16. The method according to claim10, wherein the edge offset correction filter, for at least some valuesof grey, also changes the grey value.
 17. The method according to claim10, wherein the edge offset correction filter is a rule-based filter.18. A method of preparing fine patterns to be printed with an SLMprojected through an optical path and projection optics pupil,comprising the actions of: rasterizing an input pattern to a grayscalebitmap, applying an edge offset correction filter to at least twoaligned pixels, including at least one pixel having a grey value andlight value pixel or a dark value pixel, wherein values of the edgeoffset correction filter substantially minimize the difference in theFourier transform from projecting radiation from the aligned pixels ofthe SLM and a perfect binary mask or phase shifting mask over theprojection optics pupil.